This site is dedicated to the mathematical and scientific study of ancient and modern structures, which traditionally have fallen under the category of “Sacred Geometry” or “pseudo-science.” This includes the geometric analysis of crop circles and megalithic monuments, as well as an exploration of the connections with fractals, harmonics and non-linear resonance.

Wednesday, February 10, 2016

So I’ve been sucked into the History Channel’s show The Curse of Oak Island because it combines two things I love – the hunt for treasure, and geometry. More than a year ago, I hypothesized that Oak Island had been shaped by people in order to conform to certain geometric principles. I have since found significant geometric evidence that suggests the whole eastern part of the island has been modified in the past, and was thrilled to discover in season 3 that Fred Nolan believes this as well, but for different reasons.

The logical starting point for the study of Oak Island’s geometry is Nolan’s Cross, which consists of 6 large stones placed on the island in a cross formation. Thanks to Fred Nolan’s early surveys, we have good measurements that give us the actual layout of the cross. A Norwegian man named Petter Amundsen proposed slightly different measurements, but based on my analysis, I believe Nolan’s measurements are more accurate.

Below shows the cross with Nolan’s measurements, as well as the “distance matrix” I used to analyze them. The idea is that each distance is divided by every other distance to discover the relationship between all of them as a set. I have used this method for years to study crop circles and other megalithic monuments around the world, and have found that it is only necessary to consider the quotients > 1.

It is much easier to understand the process by looking at it visually. The diagram on the left shows the measurements from Nolan, and the one on the right shows the simplification suggested by the division matrix. I call this simplified diagram a “relational model,” and I find it useful to visualize distances as circles.

Figure 2 - Actual cross measurements vs. Relational Model

Note that the arms of Nolan’s cross are in a 6/5 ratio, meaning the long arm is about 1.2 times longer than the short arm of the cross.

Petter Amundsen appeared on the first season of Curse of Oak Island to explain the geometry of the cross. His theory, in a nutshell, is that Nolan’s Cross is part of a Tree of Life geometry, and that a cipher buried in Shakespeare texts points to the treasure being hidden under what he calls the “mercy point” on this tree. So, let’s compare the geometry of the Tree of Life with the relational model of Nolan’s cross and see if they match.

Figure 3 - Tree of Life construction and relative distances

The Tree of Life has a (long arm)/(short arm) ratio of 4/sqrt(3), which means the long arm is about 2.31 times as long as the short arm.

As previously mentioned, the (long arm)/(short arm) ratio of Nolan’s cross is 6/5, or 1.2 times as long. Geometrically speaking, the arms of Nolan’s cross are proportionally different than the arms of the Tree of Life. Armundsen tried to fix this problem by adding another data point to make Nolan’s cross longer, but even this does not fix the proportions.

This mathematical mismatch is shown below as the two diagrams are scaled and superimposed (with the Tree of Life in red, Nolan’s cross in black). The first diagram shows how Armundsen viewed it, and the gray point at the bottom is his proposed new point on the cross. The resulting 8/5 ratio is still out of proportion with the 4/sqrt(3) ratio, which basically just means the short arm of Nolan’s cross is still too long, even with the modification. In the first diagram, you can also see that the central stone of Nolan’s cross does not actually correspond to a point on the Tree of Life. The second diagram shows what happens proportionally when the short arms are scaled to fit the Tree of Life – none of the other points line up.

Figure 4 - Nolan's Cross superimposed on Tree of Life

In summary, Nolan’s cross is not geometrically compatible with the Tree of Life. There is some similarity in the placement of points along the long axis, but if the builders intended a Tree of Life, I believe they would have used the correct proportions. Geometry was obviously important to those who “constructed” Oak Island. That being said, I do believe that Armundsen was probably correct about the placement of the extra stone at the bottom of the cross, but only because it fits in with the larger geometric figures that define the shape of the island.

Before I reveal how the shape of the island was changed, I want to take a closer look at Nolan’s cross, because it is critical to understanding the overall geometry of the island. Nolan’s cross is like the island’s legend, because it provides both scale and direction. The integers 1, 2, 3, 4, 5, and 6 are encoded into the cross, but it is done so in a mathematically elegant way.

This is what I see when I look at Nolan’s cross…

Figure 5 -Circular interpretation of Nolan's Cross

Each circle serves a purpose, and there is a lot going on mathematically, considering there are only 6 points. This seems familiar to me, and I need to look back into my crop circle research to see if this same pattern has turned up somewhere before. The beauty of mathematics is that it allows us to empirically compare two designs.

Let’s switch gears, and look at the rectangles that compose the cross. I am still not finished with my analysis here, because it involves the larger geometry of the island, but I have noticed one interesting property that is indicative of megalithic monuments, and architecture in general. The outer proportion of the cross is repeated on the inside, in a non-trivial manner. In the diagram below, the shaded blue rectangle is geometrically similar to the outer blue rectangle around the cross, which means the inner proportions reflect the outer. This idea can be found in Mayan/Incan cultures as well as Templar geometry.

Figure 6 - Inner and outer proportions of Nolan's Cross

In summary, I believe that Nolan’s cross is not related to the Tree of Life, but provides 1) scale and 2) direction relating to the larger geometric construction of the island. The scale, based on the distance matrix in Figure 1, is 1:145ft, which gives us a way to analyze the island in terms of pure number, as well as actual distance on the ground. When I talk about direction, I believe the cross is rotated 30 degrees from a North/South orientation, but I need to confirm this. Also, the arms of the cross provide an AXIS along which the centers of the circles that define the island are placed. The whole island screams GEOMETRY.

My next blog will show the larger geometry of Oak Island, but this is very much a work in progress, and I do not have the GPS coordinates for the stones, or other key markers, otherwise I could move a lot faster on this. In addition to Oak Island being altered, I believe the long skinny island right next to it, as well as Birch Island have been modified as well.

About Me

The author has a B.A. degree in Mathematics from Humboldt State University. She has been a Peace Corps Volunteer in Nepal, and a high school geometry and calculus teacher. Most recently, she worked in the predictive modeling industry building statistical models that rank credit risk.